2. 1(2) (2)3 3(4) n(n + 1) (n+ 1) for all natural numbers n.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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#2
Use k and (k+1)
Transcribed Image Text:9:42
AA A learn-us-east-1-prod-fleet01-xythos.c
Section 3.1 Homework
1. l'+2' +. +n' - {n°(n + 1)² for all natural numbers n.
2. 1(2) (2)3 3(4)
n(n + 1) (n + 1) for all natural numbers n.
3. Show thate
1-r for any r'1 and any nEN
4. 1+2+2 +. + 2" - 2" -1 for all natural numbers n.
5. s* -1 is a multiple of 8 for all natural numbers n
6. 9* -4" is a multiple of 5 for all natural numbers n
7. Use induction to prove Bernoulli's inequality: If 1+ x > 0, then
(1+ x)" 21+ nx for all natural numbers n
8. Prove the Principle of Strong Induction:
Let P(n) be a statement that is either true or false for each natural
number n.
Then P(n) is true for all n, provided that
(a) P(1) is true
(b) For each natural number k, if P(j) is true for all integers j such
that's jsk, then P(k + 1) is true.
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